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RE: st: left censoring in discrete-time duration model

From   "Daniel H. Simon" <>
Subject   RE: st: left censoring in discrete-time duration model
Date   Fri, 17 Nov 2006 07:25:30 -0500 (EST)

Stephen - thanks for the comments. I just want to follow up with one more
question. I am not currently trying to incorporate unobserved
heterogeneity. Regarding the concerns raised by Jason Yackee, there do not
appear to be great differences between those that establish websites
before I can observe them, and those that appear later. So, I think I can
reasonably treat the censoring as being independent. In this case, is
dropping the relevant observations a reasonable fix (and in my case,
showing that it has little effect on the results)?  thanks. Daniel

>> Date: Thu, 16 Nov 2006 13:57:13 -0500
>> From: Daniel Simon <>
>> Subject: RE: st: left censoring in discrete-time duration model
>> Stephen - first let me say that I have  consulted your
>> website materials
>> for a variety of issues and found them extremely useful.
>> Regarding your
>> comment, this is part of what has had me confused: whether
>> it's truncation
>> or censoring.  As you suggest, magazines become at risk of
>> establishing a
>> website "the later of either the year web
>> technology became available or the year when the firm itself was
>> established." But, in some cases, they establish a website
>> before I can
>> observe it. So, this sounds like truncation. If so, my
>> question is: using
>> your easy-estimation methods, which observations do I throw away. In
>> particular, in my case, do I throw away all observations for
>> 1996? 1996 is
>> the first year of the analysis period because it is the first
>> year in which
>> I observe which magazines have websites. But, I have no way
>> to distinguish
>> those magazines that had websites before 19996 and those that
>> did not.
>> After 1996, I can tell which magazines adopted new websites
>> (by comparing
>> whether they already had one the year prior). I hope this
>> makes sense.
>> thanks again for the help. Daniel
> "establish a website before I can observe it" is a classic case of
> left-censoring -- see e.g. Klein & Moeschberger, _Survival Analysis_,
> who also provide an expression for the likelihood contribution in this
> case.
> This definition of left-censoring differs a bit from the one in common
> use in the social sciences -- left-censoring referring to all cases in
> which the date of the start of the spell is unobserved.  In this
> situation, it is often recommended to drop these cases -- implicitly
> appealing to some sort of independence assumption. After all, what
> else can one do without the information? But there are potential
> problems -- of the sort raised by Jason Yackee <>
> -- if spell length (time to event) and start date are systematically
> related.
> You may have left-censoring (classical sense) and left truncation.
> Whatever the case, estimating a model incorporating unobserved
> heterogrenity (frailty) is probably harder than you'd hoped. As I
> said, I doubt whether an 'easy estimation' method is available.
> Stephen
> -------------------------------------------------------------
> Professor Stephen P. Jenkins <>
> Institute for Social and Economic Research
> University of Essex, Colchester CO4 3SQ, U.K.
> Tel: +44 1206 873374.  Fax: +44 1206 873151.
> Survival Analysis using Stata:
> Downloadable papers and software:
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